Can't Seem To Get It Right: Solving Centripetal Acceleration Equation

[scavok]

What I'm doing seems like it should work, but I can't seem to get it right. I'm sure I'm doing the math right, but I have a feeling I'm answering something that's not being asked. I would just like some help on setting up the equation right.

A car starts from rest on a flat circular track of radius 200.1 m and accelerates tangentially at a rate of 4.79 m/s². How much time elapses before the centripetal acceleration of the car is equal in magnitude to the tangential acceleration.

I have the tangential acceleration (a_t), and radius (r).
Using the centripetal acceleration equation a_c=v²/r, I set a_c=4.79 m/s², r=200.1m, and solve for the velocity.

I then use the circular motion period equation (v=(2*pi*r)/t), plug in the velocity I just calculated, the radius of the track, and solve for time.

I get 40.61s everytime, which is incorrect.

vv I got it now. Thanks for saving my hair.

 

[andrewchang]

that's not the right equation; you should be using kinematics/rotational kinematics to find the time that it accelerates. The T in that equation is for period.